Softly broken $\mu\leftrightarrow\tau$ symmetry in the minimal see-saw model

TL;DR

This paper explores how a softly broken mu-tau symmetry in a minimal see-saw model can explain neutrino mixing angles and mass differences, providing testable predictions based on radiative corrections without requiring new physics.

Contribution

It demonstrates that mu-tau symmetry can be imposed at the Lagrangian level with minimal breaking, leading to specific predictions for neutrino mixing parameters through radiative effects.

Findings

Predicts small but measurable deviations in neutrino mixing angles.

Links neutrino mass hierarchy to observable mixing deviations.

Provides a framework for testing new physics via neutrino experiments.

Abstract

Neutrino oscillations data indicates that neutrino mixings are consistent with an apparent $\nu_\mu - \nu_\tau$ exchange symmetry in neutrino mass matrix. We observe that in the mininimally extended standard model with the see-saw mechanism, one can impose $\mu\leftrightarrow\tau$ symmetry at the tree level on all Lagrangian terms, but for the mass difference among $\mu$ and $\tau$ leptons. In the absence of any new extra physics, this mass difference becomes the only source for the breaking of such a symmetry, which induces, via radiative corrections, small but predictable values for $\theta_{13}$, and for the deviation of $\theta_{ATM}$ from maximallity. In the CP conserving case, the predictions only depend on neutrino mass hierarchy and may provide a unique way to test for new physics with neutrino experiments.